The analysis of beta diversity (inter-habitat diversity) of very species-rich and incompletely sampled tropical arthropod communities requires the choice of appropriate statistical tools. The performance of the three commonly employed ordination methods, correspondence analysis (CA), detrended correspondence analysis (DCA), and non-metric multidimensional scaling (NMDS), was compared on a large empirical data set of geometrid moths sampled along an altitudinal gradient in an Andean montane rain forest. Despite the high species richness and incompleteness of the ensembles, all methods depicted the same, readily interpretable patterns. Both CA and NMDS showed an arch-like structure, which hints at an underlying coenocline, whereas this arch was computationally eliminated in DCA. For this particular data set, CA and NMDS both provided convincing results while the detrending algorithm of DCA did not improve the interpretability of the data. Of the large number of similarity indices available to be used in combination with NMDS, the binary Sørensen and the abundance-based Normalized Expected Species Shared (NESS) index were tested. Performance of the indices was measured by comparing stress, a measure of poorness-of-fit in NMDS. NMDS ordinations with lowest values of stress were achieved by the NESS index with the parameter m set to its maximum (mmax). In contrast, ordinations based on NESS values with the parameter m set to 1 (identical with Morisita's index), had consistently higher stress values and performed worse than ordinations using Sørensen's index. Hence, if high values of m can be achieved in similar data sets, the NESS index with mmax is recommended for ordination purposes and Morisita's index should be avoided.
Detrended correspondence analysis: A useful tool to quantify ecological changes from fossil data sets